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Block #2,676,545

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/24/2018, 10:58:45 PM Β· Difficulty 11.6976 Β· 4,160,370 confirmations

1CC
Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header
Block Hash
d4de4841caa69292af73fa6357ecc308061b7ba06eb97a41ac62522b42b8ab12
View on Chainz β†—

Height

#2,676,545

Difficulty

11.697563

Transactions

1

Size

201 B

Version

2

Bits

0bb2937b

Nonce

263,064,227

Timestamp

5/24/2018, 10:58:45 PM

Confirmations

4,160,370

Mined by

⛏️ P2SHAVpziFvjWhnkKRPMRkFWmBAoFdKydaFdRB

Merkle Root

f5ff92296cd2755934d6ac47b9b094b2ace24619a01aded714d2261e9cc1195f
Transactions (1)
Coinbasef5ff92296cd275…d2261e9cc1195f
1 in β†’ 1 out7.3000 XPM110 B
AVpziFvj…KydaFdRB
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.008 Γ— 10⁹⁷(98-digit number)
10088620067345405615…94409821814799631359
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin βˆ’ 1
1.008 Γ— 10⁹⁷(98-digit number)
10088620067345405615…94409821814799631359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.017 Γ— 10⁹⁷(98-digit number)
20177240134690811230…88819643629599262719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.035 Γ— 10⁹⁷(98-digit number)
40354480269381622460…77639287259198525439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.070 Γ— 10⁹⁷(98-digit number)
80708960538763244921…55278574518397050879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.614 Γ— 10⁹⁸(99-digit number)
16141792107752648984…10557149036794101759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.228 Γ— 10⁹⁸(99-digit number)
32283584215505297968…21114298073588203519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.456 Γ— 10⁹⁸(99-digit number)
64567168431010595937…42228596147176407039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.291 Γ— 10⁹⁹(100-digit number)
12913433686202119187…84457192294352814079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.582 Γ— 10⁹⁹(100-digit number)
25826867372404238374…68914384588705628159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.165 Γ— 10⁹⁹(100-digit number)
51653734744808476749…37828769177411256319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.033 Γ— 10¹⁰⁰(101-digit number)
10330746948961695349…75657538354822512639
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the First Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,939,614 XPMΒ·at block #6,836,914 Β· updates every 60s
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